One thing to note is that while all rigid-body transforms are invertible, not all transforms are. For example, the transform that maps all points to the origin (a 3x3 matrix of zeroes except for 1 on the bottom right) has no inverse.
One thing to note is that while all rigid-body transforms are invertible, not all transforms are. For example, the transform that maps all points to the origin (a 3x3 matrix of zeroes except for 1 on the bottom right) has no inverse.